#### Dividing decimals

Once again, the importance of manipulating decimals within a real-life context can be useful.

If we bought a length of rope 183.5 metres long, how many 5 m pieces could we cut from it?

When setting out the division algorithm, aligning the decimal point plays an important role. We set out the division as for whole numbers. When we get to the decimal point, we insert it in the solution, so it aligns with the number we are working with:

 3 6 . 7 5 ) 1 8 $$^3 3$$ . $$^3 5$$

183.5 ÷ 5 = 36.7 so we can cut 36.7 of the 5 m pieces. In a real-life situation we would say we have cut 36 of the 5 m pieces, with 0.7 m of 5 m left over.

For 175 ÷ 4 we use our understanding of decimals to continue the division. After the whole number we write a decimal point followed by as many zeroes as we need. Since 175 is equal to 175.00 we are not changing the number.

 4 3 . 7 5 4 ) 1 7 $$^1 5$$ . $$^3$$0 $$^2$$0

175 ÷ 4 = 43.75

Similarly for 141.3 ÷ 6, a zero is required. Placing a zero to the right of any digits after the decimal point does not alter the value.

 2 3 . 5 5 6 ) 1 4 $$^2 1$$ . $$^3 3$$ $$^2$$0